What is the value of sin^2(22.5) ?

The value of sin^2(22.5) is (2-sqrt(2))/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin^2(22.5)

sin^{2} (22. 5^{\circ})

\frac{2 - 2}{4}

Solution steps

sin^{2} (22. 5^{\circ})

Rewrite using trig identities:

\frac{1 - cos ( 4 5 ^{\circ} )}{2}

= \frac{1 - cos ( 4 5 ^{\circ} )}{2}

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

= \frac{1 - \frac{2}{2}}{2}

Simplify

\frac{1 - \frac{2}{2}}{2} : \frac{2 - 2}{4}

= \frac{2 - 2}{4}

arctan (3.7)

cos (2 \frac{5 π}{6})

cos (\frac{π}{9}) cos (\frac{7 π}{18}) - sin (\frac{π}{9}) sin (\frac{7 π}{18})

2 sin (5) cos (5)

sin (2 arcsin (- \frac{5}{13}))